With 7624 battles on your account, the Frontline mode is a lot newer than you :-).

It's impossible to be sure without a screenshot but it's my best guess. The only other reason a vehicle is not ready to join a battle, is if it is uncrewed (but it should tell you quite clearly on the caroussel picture if it is), not repaired after its previous battle (which'd also be clearly indicated) or doesn't have any ammunition on board (game gives you a verbal warning through a pop-up window).

So you were here when the various rampage modes were on where we got rental tanks, and the Halloween mode last year when we got 2 special tanks, and every other special mode where we got special tanks you could only use in that special mode.

You more than likely have a T-44 FL and a T32 FL in your garage, these are meant to be used in the Frontlines game mode.

^ This is the most likely explanation. In this case the tanks have a Frontline symbol in the tray icon. They can only be used for the new Frontline mode. To access Frontline, you need to select it as your active Battle mode.

You know when you start the game and you get that launcher come up? I know it's very annoying and just another thing you have to click to get on with the game but it does contain lots of news items which it pays to read.

Rental Vehicles
To make the event and its rewards available to as many players as possible, we are introducing two special vehicles that will allow all players to participate in the mode, regardless of whether they have a Tier VIII vehicle or not. The special vehicles are the T-44, Tier VIII U.S.S.R. medium tank and the T32, Tier VIII U.S.A. heavy tank.

If a player already has these vehicles in their Garage, the special vehicles will still be added to their account. Thus, a player may have two instances of the T32 tank in the Garage.

These rental vehicles will be available only for the Frontline mode. The vehicles will be removed from the accounts when the event is over.